Fundamental Limits in Measuring the Anisotropic Rotational Diffusion of Single Molecules

Area of Science:

• Biophysics
• Nanoscale Science
• Molecular Imaging

Background:

• Biophysical techniques often assume isotropic rotational diffusion, simplifying analysis but ignoring real-world molecular motion.
• Anisotropy in biomolecule diffusion is common in biological systems and affects nanoscale processes.
• Existing methods may not fully capture the complex rotational dynamics of molecules.

Purpose of the Study:

• To develop a theoretical framework for describing and measuring anisotropic rotational diffusion using fluorescence imaging.
• To provide a method that loosens the assumption of isotropic diffusion in biophysical measurements.
• To enable more accurate quantification of molecular processes at the nanoscale.

Main Methods:

• Established a theoretical framework for anisotropic rotational diffusion using fluorescence imaging.
• Quantified anisotropic wobble using eigenvalues of a matrix M derived from molecular transition dipole moments.
• Modeled shot noise influence using a Hermitian perturbation matrix E and Weyl's inequality.

Main Results:

• Anisotropic wobble is quantified by eigenvalues of matrix M.
• Shot noise introduces errors bounded by eigenvalues of perturbation matrix E.
• Anisotropic wobble measurements are more sensitive to errors than isotropic ones, with shot noise potentially causing measurement failure.

Conclusions:

• The developed formalism accurately describes and measures anisotropic rotational diffusion.
• Understanding shot noise effects is crucial for accurate anisotropic wobble measurements.
• This work offers insights for enhancing single-molecule orientation and diffusion imaging techniques.